Philosophy Discussion Forums | A Humans-Only Club for Open-Minded Discussion & Debate

[Jonathan A Bain]

An ellipse always returns to its starting point. Are you saying orbits are not ellipses?

Well, no, in my post back there I wasn't saying that. I was asking you a question. But since you ask, no, orbits generally are not ellipses. That's Kepler's idealisation for two body systems. If orbits were all perfect ellipses then Neptune would not have been discovered, because its discovery was due to calculations based on observations of orbital perturbations of already known planets using Newton's (not Kepler's) laws.

So a more general solution is the application of Newton's laws and a more general solution than that is Einstein's laws. As you know, the application of those laws to systems of three bodies or more has to be numerical, using finite time steps.

Clearly a situation in which a large body impacts with another large body and they both partially or wholly vapourize and/or break into an extremely large number of pieces is not a simple two body problem. So, although this doesn't in itself show your conclusion to be wrong, I don't think that the justification for that conclusion is that a body following an elliptical path always returns to the same point. We know, for example, that it is dynamically possible, in an orbital system described by Newton's laws, for a body to be ejected from that system such that it never returns.

Your recollection is likely not based on real gravity equations, rather there are vague diagrams originating from centuries past wrongly depicting a cannonball going into orbit.

I'm pretty sure they're based on modern computer simulations of Newton's laws applied to large numbers of mutually gravitating particles. I've written some simpler ones myself at various times. More complex ones appear to have been used to model collisions of large bodies to show such things as the formation of ring systems and satellites. I'll try to find some examples online, but there have been numerous gravitational simulations written over the years.

...you talk about using a "quantum of time". I presume what you're talking about here is simply the use of a finite (small but non-zero) time step in the calculations? This is what is done in all numerical computer simulations of physical systems which can't be solved analytically. Not just planetary orbits. It's also used in physics engines in computer games.

To start writing a numerical simulation of many mutually gravitating bodies is essentially quite simple. It's a numerical solution to Newton's law of gravitation:

F = Gm₁m₂ / r²

For each time step, and for each body, as an initial first order approximation, you simply work out the acceleration of each body using the above equation and F = ma, add the acceleration to the velocity and add the velocity to the position. This is the simplest possible form of numerical integration. Then you can start optimising by using higher order numerical integration methods like Runge–Kutta methods and so on.

As far as I can tell from your explanation on your website, this first approximation is what you did. It is a standard first approximation for solutions to this kind of system. I can see why you used the thing you refer to as a "holding matrix" in order to calculate all momentum changes before calculating all position changes, but I don't think this is a fundamental innovation. It doesn't alter the fact that the number of gravitational interactions to be calculated is proportional to the square of the number of bodies ((n² - n) / 2, I think), and it doesn't alter the fact that the accuracy of the model will always be dependent on the size of the finite time step chosen and the method of numerical integration chosen.

There are various other more complex algorithms, such as "particle-in-cell" algorithms, and various special case simplifications, that can reduce the required computing time for very large systems of particles such that it doesn't increase with the square of the number of particles. But there's always a trade-off between general applicability, accuracy, computing time and complexity of the algorithm.

Although not exactly the question of this topic, solving for n-body-gravity with numerous interacting gravity fields is actually a far more advanced algorithm than a single body orbit -which can only be an ellipse, or the object reaches escape velocity.

It's not necessarily a more advanced algorithm. The difference is in the way in which the problem can be solved: numerically or analytically. In an analytical solution to a problem, it is possible to write an equation that precisely defines the entire state of the system at any time t:

State = F(t)

In three-or-more-gravitating-body problems this cannot be done. Instead, the system has to be evolved from an initial time, t₀ by numerical integration.

But, at heart, the algorithm representing the numerical solution to the problem is pretty simple. It's the successive optimisations of the algorithm, and/or the use of simplifying assumptions for special cases, to yield more accurate models for a given amount of computing time that adds the algorithmic complications. As a general rule, if computing time is unlimited, algorithms can be relatively simple.

The interesting part, I think, is when you start to think about chaotic systems in which the inaccuracies of numerical solutions to problems blow up so large so quickly that no amount of computing power can keep up. But I guess that really is straying off topic.

Thank-you very much for you detailed reply.
I agree with most of your points, but you need to go back to my original post to see
my objection. But I'll just reword it, and expand on it for your convenience:

The typical answer makes no mention of extra bodies/debris and how they could interact
to form the moon and its orbit after the Mars-like object allegedly impacted the Earth.

My initial point was that such a fourth body (at least) is essential in generating a lunar orbit
because a singular body can only return to its origin or be ejected beyond Earth's orbit
due to excessive velocity. (Above escape velocity).

The real problem here is that ALL moons would have had to form through such
a many-body interaction. And the result would be orbits of various angles, directions
and eccentricities. But the reality is that most major moons orbit in a uniform direction,
on a mostly flat ecliptic plane, and are VERY close to having circular orbits too.
And while such is possible (but rare) for one moon, it is statistically almost impossible that
all major moons have such uniformity to their orbits if they formed from such chaotic collisions.

Comets are eccentric and of a wide variety of directions, so they did have chaotic impact origins,
and if there was a circularising emergent property from gravity - comets would not have such
eccentric orbits! Moreover my algorithms clearly show there is no such emergent property
purely from gravity.

You ask for my reference and, yes, it is my algorithms which were first published
online more than 10 years ago. All other such n-body-gravity algorithms I have see are like
the one you found of mine: without exact time and space scales.

I currently have such a 3d-n-body-gravity algorithm under construction which has
exact time and space scales. The process is nearly complete, and I will be publishing
some astounding results as well as computer code, hopefully within the next
couple of months. I am just currently doing the tedious task of triple-checking
those results and writing the worded article. I will certainly post the link in this
section of this forum as soon as it is ready. (If I am allowed to).

As for Einstein.
He was just wrong, and my proof is currently ranked 1st out of 15+million
at google for the keywords "instant gravity proof".

I am not allowed to post links (because I am a newbie?), so its virtually impossible
for me to give you better references than that.

That article and algorithm was written partially in response to the LIGO experimental
data and theory, and partially it was written prior to those great experiments
(but wrong physics theory) which took away the 2017 Nobel prize from under my nose.
And in all humbleness, as is possible here, I claim that prize as rightfully mine.

As for the formation of the moon!
Well, I can only get back to that when and if I can post links.

[Mans]

The moon is the result of an old explosion which happened in earth and it is not an artificial things.

[Sculptor1]

Natural Things - trees, goats, rivers

Man-made (or extraterrestrial-made) things - chairs, jet engines,... the moon?

Now this sounds like nonsense, that the moon isn't a product of nature. But look at a solar eclipse. Ever notice how astoundingly precise the position of the sun, moon, and earth must be for the moon to cover the sun so perfectly so that only the corona is showing?

I am reliably informed that the moon is made of cheese.
As soon as you can find the cow that gave the milk for all that cheese to be made, we will ahve proven the truth.

[Steve3007]

The typical answer makes no mention of extra bodies/debris and how they could interact
to form the moon and its orbit after the Mars-like object allegedly impacted the Earth.

My initial point was that such a fourth body (at least) is essential in generating a lunar orbit
because a singular body can only return to its origin or be ejected beyond Earth's orbit
due to excessive velocity. (Above escape velocity).

As I said in my previous post, a collision between a Mars-sized body and a proto-Earth is a numerous-multi-body problem. All serious treatments of the problem are models of this. The one I posted was just a YouTube video of one of them that I found from a quick Google. There are published scientific papers showing the maths behind these models if you're interested. (Numerical Analysis is a large subject in mathematics.)

The real problem here is that ALL moons would have had to form through such
a many-body interaction. And the result would be orbits of various angles, directions
and eccentricities. But the reality is that most major moons orbit in a uniform direction,
on a mostly flat ecliptic plane, and are VERY close to having circular orbits too.

The most likely reason for the near circular orbits of most planets and moons is that elliptical orbits will tend to interact with each other either by direct collisions or strong perturbations. As the early Solar System developed near-circular orbits would have been the survivors of a selection process.

You ask for my reference and, yes, it is my algorithms which were first published
online more than 10 years ago. All other such n-body-gravity algorithms I have see are like
the one you found of mine: without exact time and space scales.

As I said in my previous post, like yours and mine, they do use finite time-step numerical integration but they use more sophisticated Runge–Kutta methods than the simple Euler method that we have used and they use various optimisations to reduce the number of calculations required for the thousands of individual gravitating bodies involved.

I currently have such a 3d-n-body-gravity algorithm under construction which has
exact time and space scales. The process is nearly complete, and I will be publishing
some astounding results as well as computer code, hopefully within the next
couple of months.

Sounds interesting. I look forward to it.

As for Einstein.
He was just wrong, and my proof is currently ranked 1st out of 15+million
at google for the keywords "instant gravity proof".

A bold claim! Bold claims like that are interesting, and very common on this board over the years. There have been many, many posters who have been absolutely convinced that they alone have solved a problem or overturned a theory that has stood intact for decades or centuries and that their efforts have been deliberately overlooked by the "establishment" or "elities", as I believe it's currently fashionable to call them. It's always possible that one of them may turn out to be right. You never know. You might be the one!

Anyway, here's a link to the first hit for "instant gravity proof":

https://astronomy.stackexchange.com/que ... tantaneous

I'll take a look at it.

That article and algorithm was written partially in response to the LIGO experimental
data and theory, and partially it was written prior to those great experiments
(but wrong physics theory) which took away the 2017 Nobel prize from under my nose.
And in all humbleness, as is possible here, I claim that prize as rightfully mine.

I look forward to reading enough of your defence of that claim as time allows.

[Steve3007]

As for Einstein.
He was just wrong, and my proof is currently ranked 1st out of 15+million
at google for the keywords "instant gravity proof".

Here's a link to the second hit for "instant gravity proof":

http://www.flight-light-and-spin.com/pr ... ravity.htm

That one has your name at the bottom of it, so I suspect it's the right one. Either this is a function of our different locations when googling, or you've been slightly demoted. But I guess 2nd out of 15 million is still good.

[Nobelium]

1. The Weak Anthropic Principle states that, if a planet like Earth and a universe like ours is the only one that could support life, life should not be surprised to find itself there.

2. Regardless of the moon's size, it will be capable of creating a solar eclipse. This is because, from a certain angle, every eclipse is a full eclipse. It depends on how far away you are from the moon and at what angle it is blocking the sun's light for you.

[Sculptor1]

1. The Weak Anthropic Principle states that, if a planet like Earth and a universe like ours is the only one that could support life, life should not be surprised to find itself there.

2. Regardless of the moon's size, it will be capable of creating a solar eclipse. This is because, from a certain angle, every eclipse is a full eclipse. It depends on how far away you are from the moon and at what angle it is blocking the sun's light for you.

Point 2 - you have missed the point. There are NO other examples in the solar system where the moon is so large and the distance from the sun so exquisitely in balance that the moon can completely and exactly obscure the sun. Were the moon further away, or smaller the sun would be visible either side of the edge of the moon.
This is unique to this moment in history - as the moon gets further away the moon shall not be able to do this.

[Jonathan A Bain]

As I said in my previous post, a collision between a Mars-sized body and a proto-Earth is a numerous-multi-body problem. All serious treatments of the problem are models of this. The one I posted was just a YouTube video of one of them that I found from a quick Google. There are published scientific papers showing the maths behind these models if you're interested. (Numerical Analysis is a large subject in mathematics.)

The most likely reason for the near circular orbits of most planets and moons is that elliptical orbits will tend to interact with each other either by direct collisions or strong perturbations. As the early Solar System developed near-circular orbits would have been the survivors of a selection process.

The other problem with the Mars theory, is that there are infinite ways for collisions and n-body interactions to form an Earth-moon system.

A simple example would be two objects about half-moon size colliding near the Earth, and if the one has greater momentum, then that can ive the resultant velocity required for the orbit.

If you reckon the impact might cause some mass to be lost, that's fine and possible - then that just requires they were a bit larger.

Another easily verifiable possibility is that the moon floated past and another object simply dragged it into orbit, but then that object itself was moving fast enough to be lost to the system.

Thus, you do not need esoteric math to realize that the mars-like scenario is clearly pure conjecture which has become scholastic dogma. Even though it is still a viable scenario in itself. But it still ignores the other moons of the solar system.

As for the idea that "direct collisions or strong perturbations" can cause a concentric system with an ecliptic plane, that is once more
simply not possible except in an extreme set of coincidences.

But even if we assume (for the sake of argument) that it is true why then does this no apply to our moon? Think about it in the broader context.

There are n-body algorithms other than mine nowadays, even though I built my first one in 2008 because there were none online (that I could find) back them.

The possibility of any n-body interaction forming anything like an orbit is less than 1 in a 1000 by far, with 999 or more chances of orbits being destroyed by such random interactions.

So the result of random interactions will not be a uniform solar system. (I'll back this up with more detail when I am allowed to post links).

I can only implore you to either spend some time observing such algorithms directly or (better still) write your own algorithm and you will see for yourself directly.

As for Einstein.
He was just wrong, and my proof is currently ranked 1st out of 15+million at google for the keywords "instant gravity proof".

A bold claim! Bold claims like that are interesting, and very common on this board over the years. There have been many, many posters who have been absolutely convinced that they alone have solved a problem or overturned a theory that has stood intact for decades or centuries and that their efforts have been deliberately overlooked by the "establishment" or "elities", as I believe it's currently fashionable to call them. It's always possible that one of them may turn out to be right. You never know. You might be the one!

Thank you, all I ask is for the assessment to be based on logic, and not on 'argument from authority' (long live the philosophers!)

You may have visited stackexchange alot, so it is possible that google has elevated it for you personally. I have looked at the search from a variety of angles, and all the other people I boast to about it, confirm my position.

That article and algorithm was written partially in response to the LIGO experimental data and theory, and partially it was written prior to those great experiments (but wrong physics theory) which took away the 2017 Nobel prize from under my nose. And in all humbleness, as is possible here, I claim that prize as rightfully mine.

I look forward to reading enough of your defence of that claim as time allows.

The sheer fact of the matter is that if gravity takes 5 hours to travel between the Alpha Centauri binary they will separate at 1.4 million km per orbit, due to a gap between their positions of departure and arrival for the gravity of around 40000-50000km. That amount should be easy enough
to verify with simple arithmetic.

The 1.4 million km per orbit rate of separation does require a more complex algorithm, however. But once you see that the gap is that big, it must be realized that only a outwards spiral is possible, giving any such binary a life-span of less than a million years at best. So gravity must be instant.

Even the moon will separate from Earth at a radical rate of 400m per orbit with gravity moving at light-speed.

I can only implore you take my articles as inspiration to verify the details yourself in your own algorithms. That is the only way anyone can claim knowledge in a truly logical positivist epistemology.

[Steve3007]

On the subject of General Relativity and the finite speed of propagation of gravity:

The sheer fact of the matter is that if gravity takes 5 hours to travel between the Alpha Centauri binary they will separate at 1.4 million km per orbit, due to a gap between their positions of departure and arrival for the gravity of around 40000-50000km. That amount should be easy enough
to verify with simple arithmetic.

I read a little of the article that you wrote which you claim to be a proof that gravity acts instantaneously. It's an interesting idea but I've read that it was already thought of by Laplace in 1805.

https://en.wikipedia.org/wiki/Speed_of_gravity#Laplace

Like you, and for the same reasons, Laplace concluded that orbiting bodies would gradually recede from each other. The reasons why this analysis is incorrect have been shown during the 19th and 20th centuries by various people. It is a simple Newtonian force concept of finite-velocity gravity, but more modern theories of gravity do not use the Newtonian concept of a force in this way. In a theory which invokes the concept of gravitational waves and not Newtonian forces acting at a distance the problem that you and Laplace identified does not occur.

At least, that's what I've read.

If you want to discuss this particular subject further I guess it's probably best to start a new topic as it's strayed quite a long way from the original subject of this one, although I should say that I'm no expert on the details of General Relativity so will only be able to put to you my crude understanding of the arguments of specialists in the field that I've read and the little that I dimly remember from university.

I'll reply to your further comments about the formation of the moon separately. I've written various simple crude simulations of n-body gravity simulations myself, starting in the 1980's on my old ZX Spectrum! Those were very crude and simple. Modern PCs, with clocks running 1000's of times faster, allow a little more sophistication. I wrote a 2048 body simulation a while ago that I'll try to post on here if I get time. I'll post a bit of the code (written in C#) if you like. As I understand it, much more mathematically rigourous academic simulations of such systems have been written since at least the 1970's.

[Steve3007]

Just so that we know we're on the same page, here's a bit of simplified C#-style code showing some the core functionality of my more recent gravity simulations. As you can see, it simply calculates the Newtonian force between every body and every other body and uses the very simple Euler method to do the numerical integration. For the sake of brevity, this snippet misses out a lot. It doesn't contain the code which deals with collisions between bodies and it doesn't scale the time. It just implicitly assumes a time-step of 1 second. To deal with collisions between bodies, the full code attempts to model partially elastic collisions which conserve momentum but only partially conserve energy. The energy lost due to the collisions being only partially elastic is used to heat up the bodies. Visually, when the simulation is displayed on a screen, each body's temperature is represented using colour. As well as increasing in temperature during collisions, each body conducts heat to neighbouring bodies with which it is in contact and radiates heat energy to space.

Code: Select all

const float G = 6.67408e-11;
const int num_bodies = 2048;

Vector[] position = new Vector[num_bodies];
Vector[] velocity = new Vector[num_bodies];
float[] mass = new float[num_bodies];

// TODO: Give these bodies some positions, velocities and masses

while(true)
{
    // For each pair of bodies
    for(int i = 0; i < num_bodies - 1; i++)
    {
        for(int j = i + 1; j < num_bodies; j++)
        {
           // Get a vector which represents the distance from body i to body j
            Vector p = position[j] - position[i];
            // Use Pythagorus to get the square of that distance
            float r_squared = p.Length_Squared();
            // And the distance itself. Sqrt is slow. You may want to replace the Sqrt function here with a faster approximation.
            float r = Math.Sqrt(r_squared);
            // Use all this to get a unit vector in the direction of the vector from i to j
            Vector unit_vector = p / r;
            // Use Newton's law of Universal Gravitation to get the vector representing the force that each exerts on the other
            Vector force =  unit_vector * (G * mass[i] * mass[j] / r_squared);
            // Use Newton's 2nd law (F = ma), rearranged, to get the acceleration of i and j from the force
            Vector accel_i = force / mass[i];
            Vector accel_j = -force / mass[j];
            // Add the acceleration of each to the velocity of each
            velocity[i] += accel_i;
            velocity[j] += accel_j;
        }
    }

    // Now that all velocities have been calculated from all positions in this frame, 
    // go through each of the bodies again adding the velocities to the positions.
    for(int i = 0; i < num_bodies; i++)
    {
        position[i] += velocity[i];
    }
}

// Create a class to represent a vector. This class isn't essential. We could have arrays
// of floats, above, to represent the X, Y and Z components of the bodies' positions and
// velocities. But the code above would then be more longwinded and harder to read.

public class Vector
{
    float X, Y, Z;

    public float Length_Squared()
    {
        return X * X + Y * Y + Z * Z;
    }

    // TODO: Add standard overloaded operators +, -, / and *
}

[Halc]

As for Einstein.
He was just wrong, and my proof is currently ranked 1st out of 15+million
at google for the keywords "instant gravity proof".
...
which took away the 2017 Nobel prize from under my nose.
And in all humbleness, as is possible here, I claim that prize as rightfully mine.

One does not get a Nobel prize for putting out a paper describing what is common knowledge.

Gravity is a field, and hence has no speed. Einstein did not assert gravity travels at some speed (like c or anything else).
Gravity waves do (as evidenced by gravity waves from colliding neutron stars arriving just ahead of the light from the event), but gravity waves are not gravity. The Earth has enough gravity to hold me to it, but puts out only about 200 watts of gravity waves due to its acceleration due to the sun.

[Jonathan A Bain]

On the subject of General Relativity and the finite speed of propagation of gravity:

The sheer fact of the matter is that if gravity takes 5 hours to travel between the Alpha Centauri binary they will separate at 1.4 million km per orbit, due to a gap between their positions of departure and arrival for the gravity of around 40000-50000km. That amount should be easy enough
to verify with simple arithmetic.

I read a little of the article that you wrote which you claim to be a proof that gravity acts instantaneously. It's an interesting idea but I've read that it was already thought of by Laplace in 1805.

Like you, and for the same reasons, Laplace concluded that orbiting bodies would gradually recede from each other. The reasons why this analysis is incorrect have been shown during the 19th and 20th centuries by various people. It is a simple Newtonian force concept of finite-velocity gravity, but more modern theories of gravity do not use the Newtonian concept of a force in this way. In a theory which invokes the concept of gravitational waves and not Newtonian forces acting at a distance the problem that you and Laplace identified does not occur.

At least, that's what I've read.

If you want to discuss this particular subject further I guess it's probably best to start a new topic as it's strayed quite a long way from the original subject of this one, although I should say that I'm no expert on the details of General Relativity so will only be able to put to you my crude understanding of the arguments of specialists in the field that I've read and the little that I dimly remember from university.

I'll reply to your further comments about the formation of the moon separately. I've written various simple crude simulations of n-body gravity simulations myself, starting in the 1980's on my old ZX Spectrum! Those were very crude and simple. Modern PCs, with clocks running 1000's of times faster, allow a little more sophistication. I wrote a 2048 body simulation a while ago that I'll try to post on here if I get time. I'll post a bit of the code (written in C#) if you like. As I understand it, much more mathematically rigourous academic simulations of such systems have been written since at least the 1970's.

I had not realized that Laplace had made a similar point to mine. Thanks.

Yes, I'll start a new thread on that theme. (This is just a warm-up).
But it does tie into my point about the orbit of the moon.
Because you are claiming relativity can effect the formation of its orbit,
but then also claiming that relativity does not effect the orbit by
implication in that article.

The article on Laplace you offer is fairly wordy, most of which
is just waffle, and the only attempted rebuttle to the argument is this:

When an object is moving in orbit at a steady speed but changing velocity v,
the effect on the orbit is order v2/c2, and the effect preserves energy and
angular momentum, so that orbits do not decay.

That quote is sheer pseudo-science for numerous reasons:
Firstly because speed and velocity are virtually synonymous in this context
so its meaningless to suggest a steady speed with a changing velocity.

Secondly the dynamic of changing or constant speed or velocity has no
impact on the modeling. All that matters is the delay due to the distance.
So its just a matter of the direction of the pull of gravity.

The phrase "is order v2/c2" makes zero grammatical sense.
I assume it means v^2/c^2, but even then it is just random and meaningless.

Whether or not we use waves or photons does not change the nature
of the path of light, so if the gravity follows the same path at the same
velocity then its geometry is going to be identical to the light.

It seems I am still not allowed to post links, so its doubtful
I will be allowed to start a thread.

[Jonathan A Bain]

As for Einstein.
He was just wrong, and my proof is currently ranked 1st out of 15+million
at google for the keywords "instant gravity proof".
...
which took away the 2017 Nobel prize from under my nose.
And in all humbleness, as is possible here, I claim that prize as rightfully mine.

One does not get a Nobel prize for putting out a paper describing what is common knowledge.

Gravity is a field, and hence has no speed. Einstein did not assert gravity travels at some speed (like c or anything else).
Gravity waves do (as evidenced by gravity waves from colliding neutron stars arriving just ahead of the light from the event), but gravity waves are not gravity. The Earth has enough gravity to hold me to it, but puts out only about 200 watts of gravity waves due to its acceleration due to the sun.

If you turn to page 94 of Hawking's brief history of time
you will read this:

"General Relativity predicts that heavy objects that are
moving will cause the emission of gravitational waves,
ripples in the curvature of space that
travel at the speed of light."

and on page 74-75
"Real gravitons make up what classical physicists would call gravitational waves".

So the scientists certainly are claiming that gravitational waves are gravity.

(Incidentally a 'gravity wave' is entirely different to a 'gravitational wave.')
I assume you meant the latter. A 'gravity wave' is something in the ocean, actually.

The data that was measured by LIGO which WAS moving at the speed of light,
is therefore electromagnetic in origin. Not gravitational.
Even though the majority believe otherwise.

As for the reasons one gets a Nobel prize, thats another debate,
but it seems it often has little or nothing to do with a logical positivist method
and everything to do with money.

I could tell you exactly what the LIGO data measured, but I am not allowed to
post links yet.

[doberso]

What you are marvelling at is evidence of an intelligently-designed, finely-tuned universe. Why do you suspect Earth's moon and not any other heavenly body to be artificially created? Might it have anything to do with the writings of David Icke?

[Terrapin Station]

The odds of it being random are too small.

Regardless of the relative sizes, distances and motions of the Earth, moon and sun, the odds of them being whatever they'd be would be the same.

That's probably a confusing sentence, so let's explain it.

First, there's no way to say just how many different possible answers there are to what the relative sizes, distances, etc. would be. The possibilities would probably be effectively infinite, but we could just pick some arbitrarily large number. Let's use something like a "trillion trillion."

So, if the moon's apparent size were four times as large as the sun, there would be a one in a trillion trillion chance of that being the case.

Likewise, if the moon's apparent size were only a quarter as large as the sun, there would be a one in a trillion trillion chance of that being the case.

Also, if the moon's relative motion only produced partial eclipses with never more than 81% of the sun's surface being covered, there would be a one in a trillion trillion chance of that being the case.

And so on.

The answer would be the same for any set of relations that obtained. That's because only one set of relations can obtain, and for every one of them, there was only a one in a trillion trillion chance of that set obtaining.

It works just like the lottery. If there are 13 million possible combinations of numbers in a given lottery, then the chance for any arbitrary set of numbers to be chosen is 1 in 13 million. It doesn't matter what the set of numbers is. They all have an equal chance of obtaining--1 in 13 million.

So there aren't actually outcomes that are less probable than others in a situation like this. They're all equally improbable. But one has to turn out to be the configuration.